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A262427
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Decimal expansion of the complete elliptic integral of the first kind at sqrt(2*sqrt(2) - 2).
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6
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2, 3, 2, 7, 1, 8, 5, 1, 4, 2, 4, 3, 6, 5, 3, 8, 7, 5, 0, 6, 0, 5, 0, 3, 6, 2, 8, 5, 6, 1, 8, 3, 5, 7, 0, 7, 7, 5, 1, 5, 1, 8, 1, 7, 5, 8, 2, 3, 2, 5, 4, 1, 1, 7, 4, 7, 9, 3, 2, 0, 8, 1, 9, 9, 4, 4, 6, 1, 1, 8, 8, 2, 5, 7, 3, 1, 3, 6, 0, 4, 9, 5, 7, 8, 2, 2, 5, 9, 0, 0, 7, 0, 1, 1, 0, 6, 6, 1, 0, 5, 6, 2, 3, 7, 1
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OFFSET
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1,1
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LINKS
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FORMULA
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Equals Pi^(3/2)*sqrt(4 + 2*sqrt(2))/(4*Gamma(5/8)*Gamma(7/8)).
Also equals sqrt(2)*K(sqrt(2) - 1).
Also equals Pi^(3/2)*cos(Pi/4)*cos(Pi/8)/(Gamma(5/8)*Gamma(7/8)). - Christian N. Hofmann, Aug 20 2023
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EXAMPLE
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2.3271851424365387506050362856183570775151817582325411747932...
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MAPLE
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MATHEMATICA
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K[x_] := EllipticK[x^2/(x^2 - 1)]/Sqrt[1 - x^2]; RealDigits[ K[Sqrt[2 Sqrt[2] - 2]], 10, 105][[1]]
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PROG
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(PARI) ellk(k)=intnum(t=0, 1, 1/sqrt((1-t^2)*(1-(k*t)^2)))
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)^(3/2)*Sqrt(4 + 2*Sqrt(2))/(4*Gamma(5/8)*Gamma(7/8)); // G. C. Greubel, Oct 07 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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